Thousands of people have gathered in cities across Australia to protest against the Federal Government's 2014 budget.

Protesters angered by the announced budget cuts to Government services - including health and education - gathered in Adelaide, Brisbane, Melbourne, Sydney, Perth and Hobart on Sunday, as part of the nationwide March in May rallies.

In Sydney, the crowd was estimated at up to 10,000 people.

Protesters gathered in Sydney's CBD carrying placards with messages such as "hands off health, education and welfare".

Heather Williams, who works in education, said she was concerned about the Government's changes to unemployment benefits announced in the budget.

"I'm very concerned about the young, unemployed [people] under this budget," she said.

"It really worries me. I know a lot of people who tried very hard to get work."

The protest was not disruption free, with 13 people being arrested for disobeying police.

In Melbourne, the proposed cuts to assistance for unemployed young people were also in focus, as was the lifting of the pension age to 70.

"If you say to the Australian people, 'What do you think is better – asking Gina Rinehart and the big banks and the big polluters to pay a bit more or taking the axe to the young and the sick and the poor?' I know which way this country will vote," he said.

South Australian Premier Jay Weatherill says thousands of people turned out to protest in Adelaide.

"Why are 6,000 South Australians raising their voices in Adelaide today? They understand that this is about making sure when they are sick, there is a hospital bed for them," he said at a joint news conference with other state leaders in Sydney.

"When their children have a learning difficulty, there is the extra teaching support to allow their child to be a success – that's what's at stake, that's what's motivating them, and we are speaking for those Australians as we stand here today together.

"We have not seen rallies like this in SA since WorkChoices."

Some protesters travelled from regional areas to capital cities so they could take part.

"I've come down from Lithgow with my friend to meet my family here," one Adelaide protester said.

"All of us feel that we're not getting what we wanted, what we need."

In Brisbane, hundreds of people gathered for a rally at Queens Park in the CBD.

Many of the protesters were angry about the announced cuts to a number of government services and changes to education policies.

"I'm very concerned about the deregulation of university fees. I think that's really going to mean that education is for an elite rich few, which is not acceptable in our society," one protester said.

In Hobart, about 500 protesters gathered on Parliament lawns.

Rally organiser Ben Peelman says he has never seen so much anger on social media about one issue in such a short period of time.

"I think this was a very good, very accurate expression of public opinion," he said.